From: Sandro Hawke <sandro@w3.org>
Subject: Re: A Rough Guide to Notation3
Date: Sat, 24 Aug 2002 17:52:12 -0400
[Lots of tangential stuff about inconsitencies and information removed.]
> > The problem is not their (potential) existence. It is their existence
> > everywhere. The problem is that if you allow self-referential
> > sentences and also need to have sentences exists everywhere, removing just
> > the problematic ones is problematic.
>
> I don't quite follow that, sorry.
The problem with some self-referential sentences, such as the self negating
one, is that they have no models, not even models that assign them a truth
value of false.
This is not a problem for a DAML+OIL. Entailment defined on top of
DAML+OIL would be very weak, because not all DAML+OIL classes need exist in
all DAML+OIL interpretations. Mentioning the analogue of a self-negating
sentence in DAML+OIL is like stating a contradiction.
However, if DAML+OIL is to be given a reasonable notion of entailment, so
that, for example, John in Student and John in Employee entails John in the
intersection of Student and Employee, then all DAML+OIL classes must
exist in all DAML+OIL interpretations. However, this then includes the
problematic ones, which ends up with all DAML+OIL knowledge bases having no
interpretations.
Trying to forbid just the problematic classes requires something like ``A
class is acceptable syntactially if it is acceptable semantically'' which
is itself problematic.
> -- sandro
Again, there are lots of ways around this problem, just none that fit into
the strong version of the RDF philosophy.
peter